Question

Hᴇʟʟᴏ Bʀᴀɪɴʟɪᴀɴs ¡!

Answer 1

Answer:

volume: 49280 cm³  and   curved S.A = 5826.64 cm²

Explanation:

• height of smaller cone: h₂
• radius of smaller cone: 7
• height of bigger cone: 45 + h₂
• radius of bigger cone: 28

using similarities:

$\sf \frac{45 + h2}{28} = \frac{h2}{7}$

$\sf 315 + 7h2 = 28h2$

$\sf 315 = 28h2-7h2$

$\sf 315 = 21h2$

$\sf 15 = h2$

total height of the cone: 45 + 15 = 60 cm

solve for volume:

$\sf volume \ of \ cone \ = \frac{1}{3} \pi r^2 h$

$\sf volume \ of \ cone \ = \frac{1}{3} \pi (28)^2 (60)$

$\sf volume \ of \ cone \ = 15680\ *\frac{22}{7}$

$\sf volume \ of \ cone \ = 49280 \ cm^3$

First find the slant height using Pythagoras theorem -

$\sf l^2 = r^2 + h^2$

$\sf l =\sqrt{ r^2 + h^2}$

$\sf l =\sqrt{ (28)^2 + (60)^2}$

$\sf l =66.212 \ cm$

solve for curved surface area:

$\sf curved \ surface \ area = \pi rl$

$\sf curved \ surface \ area = \pi (28)(66.2)$

$\sf curved \ surface \ area =5826.64 \ cm^2$